In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of the traditional formulations of quantum field theories, namely, smooth distributions for the field commutators that are finite a short distances, finite vacuum expectation values for the energy (without invoking normal ordering of operators), and finite fluctuations for the field operators. Our construction is based on a critical point of view on conventional quantum field theory statements, instead of invoking string theory inspired frameworks, since they are not necessary. We shall show that the conventional scheme for constructing quantum field theories has the necessary ingredients for obtaining generalized versions that, respecting the Lorentz symmetry, allows us to cure some of the divergences that plague the different formulations, particularly the ultra-violet divergences; additionally the present scheme will allows us to construct an infinite family of noncommutative field theories that are compared with other formulations. At the end, we discuss the impact of our formulation on particle physics numerology and on the cosmological constant problem
The Abraham-Lorentz force is a finite remnant of the UV singular structure of the self interaction of a point charge with its own field. The satisfactory description of such interaction needs a relativistic regulator. This turns out to be a problematic point because the energy of regulated relativistic cutoff theories is unbounded from below. However one can construct point splitting regulators which keep the Abraham-Lorentz force stable. The classical language can be reconciled with QED by pointing out that the effective quantum theory for the electric charge supports a saddle point producing…
We study static and radially symmetric black holes in the multi-fractional theories of gravity with $q$-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length $\ell_*$. In the $q$-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to $\ell_*$. In the multi-fractional theory with weighted derivatives, there is no such deformat…
In this paper we construct a non-commutative geometry over a configuration space of gauge connections and show that it gives rise to a candidate for an interacting, non-perturbative quantum gauge theory coupled to a fermionic field on a curved background. The non-commutative geometry is given by an infinite-dimensional Bott-Dirac type operator, whose square gives the Hamilton operator, and which interacts with an algebra generated by holonomy-diffeomorphisms. The Bott-Dirac operator and the associated Hilbert space relies on a metric on the configuration space of connections, which effectively…
